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Journal of Reliable Power - SEL

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11<br />

Zone 1 distance elements should account for the above<br />

phenomena by reducing the reach [20][21]. A good suggestion<br />

is to set the reach <strong>of</strong> the reactive line to half <strong>of</strong> the<br />

compensated line impedance [20]. On the other hand,<br />

protective relays can have an automatic reach adjustment<br />

based on a measured apparent impedance compared to a<br />

theoretically calculated value [14][21]. This way, the reach is<br />

automatically reduced to half <strong>of</strong> the compensated line<br />

impedance when transients are detected. The resistive reach<br />

should follow the recommendations for a long line (e.g., Rset<br />

equal to one-half Zset).<br />

The presence <strong>of</strong> the series capacitor in the power system<br />

modifies the homogeneity <strong>of</strong> the negative- and zero-sequence<br />

impedances. Therefore, when adjusting the homogeneity<br />

factor T, described in (18) and (19), the capacitor impedance<br />

should be considered. When using a negative-sequence current<br />

polarized reactance element:<br />

⎛ IF2 ⎞ ⎡ ZS1 + ZL1 − XC + ZR1 ⎤<br />

T = arg⎜ ⎟ = arg<br />

IR2<br />

⎢<br />

ZR1 + (1 − m)(ZL1 − XC)<br />

⎥ (18)<br />

⎝ ⎠ ⎣ ⎦<br />

And when using a zero-sequence polarized reactance line:<br />

⎛ IF0 ⎞ ⎡ ZS0 + ZL0 − XC + ZR0 ⎤<br />

T = arg ⎜ ⎟ = arg<br />

IR0<br />

⎢<br />

ZR0 + (1 − m)(ZL0 − XC)<br />

⎥ (19)<br />

⎝ ⎠ ⎣ ⎦<br />

Notice that the zero- and negative-sequence impedance <strong>of</strong> a<br />

series capacitor are the same as the positive-sequence<br />

impedance.<br />

Equation (18) for the uncompensated line should also be<br />

evaluated. The minimum calculated T value (most negative)<br />

should be used.<br />

When applying any protective relaying scheme to seriescompensated<br />

lines, transient simulation and testing are<br />

recommended [19][21]. This step ensures dependability and<br />

confirms proposed settings.<br />

E. Single-Pole Trip Applications<br />

In transmission line protection, it is common to use singlepole<br />

trip schemes. The scheme trips the faulted phase only for<br />

a single-line-to-ground fault. Once the pole is open, the other<br />

two phases are still conducting power, and the system is<br />

capable <strong>of</strong> remaining synchronized. During the open-pole<br />

interval, it is expected that the arc deionizes. After the openpole<br />

interval, a reclosing command is sent to the breaker.<br />

Current polarization with negative-sequence current (I2) or<br />

zero-sequence current (I0) is not reliable during the open-pole<br />

interval. The open pole makes the power system unbalanced,<br />

causing negative- and zero-sequence currents to flow. The<br />

consequence to distance elements polarized with sequence<br />

component currents, as in (3) and (8), is that the polarization<br />

becomes unreliable. Depending on the load flow direction, I2<br />

and I0 will have different directions. Fortunately, there are<br />

other distance elements that will reliably operate during an<br />

open-pole condition [14]. The positive-sequence voltagepolarized<br />

mho element is stable during open-pole intervals and<br />

will reliably detect power system faults during this condition.<br />

In a practical scheme, the phase and ground quadrilateral<br />

elements should be disabled when an open-pole condition is<br />

detected. The high-speed quadrilateral distance element is<br />

implemented with incremental quantities and does not need to<br />

be disabled during the open-pole interval.<br />

IV. SETTING THE QUADRILATERAL DISTANCE ELEMENT<br />

Consider the A-phase-to-ground fault circuit <strong>of</strong> Fig. 4.<br />

Equation (20) determines the apparent impedance (Zapp) that<br />

the relay installed at the left side <strong>of</strong> the line measures as a<br />

function <strong>of</strong> fault voltages and currents. Equation (21)<br />

determines Zapp as a function <strong>of</strong> Rf and fault location m.<br />

VA<br />

Zapp =<br />

IA + k0 • IR<br />

(20)<br />

Zapp = m • ZL1 + KR • Rf<br />

(21)<br />

In (21), KR is a factor that depends upon the positive- and<br />

zero-sequence current distribution factors (C1 and C0) and is<br />

equal to:<br />

KR 3<br />

=<br />

(22)<br />

2 • C1 + C0(1 + 3• k0)<br />

C1 and C0 are equal to:<br />

(1 − m) • ZL1 + ZR1<br />

C1 =<br />

(23)<br />

ZS1 + ZL1 + ZR1<br />

(1 − m) • ZL0 + ZR0<br />

C0 =<br />

(24)<br />

ZS0 + ZL0 + ZR0<br />

k0 is the zero-sequence compensation factor equal to:<br />

ZL0 − ZL1<br />

k0 = (25)<br />

3• ZL1<br />

For no-load conditions (δ equal to 0) and homogeneous<br />

systems, the resistive blinder <strong>of</strong> the adaptive quadrilateral<br />

element will assert for an Rf that satisfies this condition:<br />

Rapp < Rset<br />

(26)<br />

Rapp = Real(KR) • Rf<br />

(27)<br />

where Rset is the resistive reach setting. Alternatively, we can<br />

calculate Rapp using relay voltage and currents for a fault at m<br />

according to (28).<br />

Rapp = Real( Zapp) − m • Real( ZL1)<br />

(28)<br />

Adaptive Phase and Ground Quadrilateral Distance Elements | 75

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